Banach April 2004

banach@mathdept.okstate.edu

2 participants
13 discussions

Abstract of a paper by Mark Rudelson and Roman Vershynin
by Dale Alspach 12 Apr '04

12 Apr '04

This is an announcement for the paper "Random processes via the combinatorial dimension: introductory notes" by Mark Rudelson and Roman Vershynin. Abstract: This is an informal discussion on one of the basic problems in the theory of empirical processes, addressed in our preprint "Combinatorics of random processes and sections of convex bodies", which is available at ArXiV and from our web pages. Archive classification: Functional Analysis; Probability Theory Mathematics Subject Classification: 46B09, 60G15, 68Q15 Remarks: 4 pages The source file(s), rv-processes-description.tex: 12005 bytes, is(are) stored in gzipped form as 0404193.gz with size 5kb. The corresponding postcript file has gzipped size 30kb. Submitted from: vershynin(a)math.ucdavis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0404193 or http://arXiv.org/abs/math.FA/0404193 or by email in unzipped form by transmitting an empty message with subject line uget 0404193 or in gzipped form by using subject line get 0404193 to: math(a)arXiv.org.

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Abstract of a paper by Takashi Itoh and Masaru Nagisa
by Dale Alspach 08 Apr '04

08 Apr '04

This is an announcement for the paper "The numerical radius Haagerup norm and Hilbert space square factorizations" by Takashi Itoh and Masaru Nagisa. Abstract: We study a factorization of bounded linear maps from an operator space $A$ to its dual space $A^*$. It is shown that $T : A \longrightarrow A^*$ factors through a pair of a column Hilbert spaces $\mathcal{H}_c$ and its dual space if and only if $T$ is a bounded linear form on $A \otimes A$ by the canonical identification equipped with a numerical radius type Haagerup norm. As a consequence, we characterize a bounded linear map from a Banach space to its dual space, which factors through a pair of Hilbert spaces. Archive classification: Operator Algebras Mathematics Subject Classification: 46L07 (Primary) 47L25, 46B28, 46L06 (Secontary) Remarks: 16 pages The source file(s), ina03.tex: 44003 bytes, is(are) stored in gzipped form as 0404152.gz with size 12kb. The corresponding postcript file has gzipped size 70kb. Submitted from: itoh(a)edu.gunma-u.ac.jp The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.OA/0404152 or http://arXiv.org/abs/math.OA/0404152 or by email in unzipped form by transmitting an empty message with subject line uget 0404152 or in gzipped form by using subject line get 0404152 to: math(a)arXiv.org.

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Abstract of a paper by Vassiliki Farmaki
by Dale Alspach 02 Apr '04

02 Apr '04

This is an announcement for the paper "Ramsey and Nash-Williams combinatorics via Schreier families" by Vassiliki Farmaki. Abstract: The main results of this paper (a) extend the finite Ramsey partition theorem, and (b) employ this extension to obtain a stronger form of the infinite Nash-Williams partition theorem, and also a new proof of Ellentuck's, and hence Galvin-Prikry's partition theorem. The proper tool for this unification of the classical partition theorems at a more general and stronger level is the system of Schreier families $({\cal A}_{\xi})$ of finite subsets of the set of natural numbers, defined for every countable ordinal $\xi$. Archive classification: Functional Analysis Mathematics Subject Classification: Primary 05D10; Secondary 05C55 Remarks: 28 pages, preliminary version The source file(s), Ramseytheorem.tex: 91989 bytes, is(are) stored in gzipped form as 0404014.gz with size 22kb. The corresponding postcript file has gzipped size 83kb. Submitted from: combs(a)mail.ma.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0404014 or http://arXiv.org/abs/math.FA/0404014 or by email in unzipped form by transmitting an empty message with subject line uget 0404014 or in gzipped form by using subject line get 0404014 to: math(a)arXiv.org.

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Banach April 2004